• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.873-892
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• 2020

Thurston, in 1986, discovered that the Schwarzian derivative has mysterious properties similar to the curvature on a manifold. After his work, there are several approaches to develop this notion on Riemannian manifolds. Here, a tensor field is identified in the study of global conformal diffeomorphisms on Finsler manifolds as a natural generalization of the Schwarzian derivative. Then, a natural definition of a Mobius mapping on Finsler manifolds is given and its properties are studied. In particular, it is shown that Mobius mappings are mappings that preserve circles and vice versa. Therefore, if a forward geodesically complete Finsler manifold admits a Mobius mapping, then the indicatrix is conformally diffeomorphic to the Euclidean sphere S^n-1 in ℝⁿ. In addition, if a forward geodesically complete absolutely homogeneous Finsler manifold of scalar flag curvature admits a non-trivial change of Mobius mapping, then it is a Riemannian manifold of constant sectional curvature.

• Journal of the Korean Mathematical Society
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• v.52 no.2
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• pp.333-347
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• 2015

In this paper, by using the modular forms of weight nk ($2{\leq}n{\in}\mathbb{N}$ and $k{\in}\mathbb{Z}$), we construct a formula which generates modular forms of weight 2nk+4. This formula consist of some known results in [14] and [4]. Moreover, we obtain Fourier expansion of these modular forms. We also give some properties of an operator related to the derivative formula. Finally, by using the function $j_4$, we obtain the Fourier coefficients of modular forms with weight 4.

• Archives of Pharmacal Research
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• v.11 no.2
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• pp.155-158
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• 1988

To study the behavior of nucleic acid base in a nonpolar organic solvent, chloreform, we synthesized a derivative of guanosine. This erivative, guanosine-2', 3', 5'- trisobutyrate was obtained by reaction of guanosine with isobutyric anhydride, and identified by TLC, EA, IR and NMR. Hydrogen bonding specificity of this compound was revealed by IR and NMR. The molecules of guanosine 2',3',5'-trisobutyrate are self-associated in nonpolar solvent, and hydrogen bonds by imino protent become important as the concentration increases. In the presence of a cytosine derivative, the self-association of theguanosine drivative is destroyed, resulting from interaction with cytosine derivative.

• Journal of the Korean Society of Clothing and Textiles
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• v.24 no.7
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• pp.1081-1087
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• 2000

Gromwell colorants were extracted with methanol and dried. Four fractions were obtained by silica gel adsorption column chromatography using step-wise elution method. Relative ratio of four fraction is 1.00:0.07:0.22:0.30(Fl:F2:F3:F4) and gromwell colorants mainly consist of Fl, F3 and F4. IR analysis shows that each fraction has similar structure. Main component of gromwell extracts is acetyl derivative of naphthoquinone, and the rest are isobutyl derivative and isovaleryl derivative etc., in order. Gromwell colorants exhibit relatively good affinity to protein and polyamide fibers, but low affinity to cellulose and regenerated cellulose fibers.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.549-560
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• 2018

Since Mittag-Leffler introduced the so-called Mittag-Leffler function in 1903, due to its usefulness and diverse applications, a variety and large number of its extensions (and generalizations) and variants have been presented and investigated. In this sequel, we aim to introduce a new extension of the Mittag-Leffler function by using a known extended beta function. Then we investigate ceratin useful properties and formulas associated with the extended Mittag-Leffler function such as integral representation, Mellin transform, recurrence relation, and derivative formulas. We also introduce an extended Riemann-Liouville fractional derivative to present a fractional derivative formula for a known extended Mittag-Leffler function, the result of which is expressed in terms of the new extended Mittag-Leffler functions.

• Bulletin of the Korean Chemical Society
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• v.21 no.11
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• pp.1152-1154
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• 2000

• Proceedings of the Korean Fiber Society Conference
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• 1989.06a
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• pp.59-60
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• 1989

• Proceedings of the Korean Fiber Society Conference
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• 2001.04b
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• pp.351-354
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• 2001

• Bulletin of the Korean Chemical Society
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• v.21 no.1
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• pp.145-147
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• 2000

• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.199-213
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• 2006

We compute the holomorphic derivative of the harmonic measure associated to a $C^\infty$bounded domain in the plane and show that the exact Bergman kernel function associated to a $C^\infty$ bounded domain in the plane relates the derivatives of the Ahlfors map and the Szego kernel in an explicit way. We find several formulas for the exact Bergman kernel and the Szego kernel and the harmonic measure. Finally we survey some other properties of the holomorphic derivative of the harmonic measure.